Find the domain and range of the function

Question

f(x)=

 

-3x-2     x less than 4

3/4x-1   x greater than or equal to 4

 

I have figured out the domain is (-infinity,infinity). I am really struggling on the range. 

Answer 1

The range of -3x-2 runs from ∞ as x→-∞ to -14 at x = 4.  The range of 3/(4x-1) runs from 3/15 at x = 4 to y→0 as x→∞.  This range is a subset of the range of -3x-2, so the range of f(x) is (-14,∞).  I used an open bracket at -14 (vice a closed one [ ) because -3x-2 applies only for x < 4, and hence the point (4,-14) is not included.